Unfortunately, this is the kind of phenomenon which, if it ever did occur, we'd almost certainly never know about. The Danes in England during the Danelaw period leave us no documentary sources of any sort, and contemporary English sources make no mention of it, nor really any non-military activities beyond establishing there being a yoke of oppression from which, of course, it was the rightful duty of the English kings to liberate their countrymen.

That said, the Danes don't appear to have been antithetical to the Christian beliefs or practices of the English under their political control. Certainly, the cult of Edmund the Martyr which sprung up in the 880s and 890s in East Anglia was at the least tolerated, if not actively endorsed, by the ruling Danes. With that in mind, it's unlikely that any English would have been coerced into renouncing Christianity and converting to a form of Norse paganism, although it's not, technically, impossible.